Here we consider three circles c_{1}, c_{2}, c_{3} belonging to the same bundle of circles I(c_{1}, c_{2}), generated by the first two of them. We draw tangents from points A of circle c_{1} to c_{2}, c_{3}, and consider the tangency chord BC. Find the equation of the envelope of lines BC. The same question when c_{1}, c_{2}, c_{3} are conics.

It seems to include formidable calculations. The case in which the two inner circles c_{2}, c_{3} coincide with one circle (c'(M,r), with M(a,0)), and c_{1} centered at the origin (c_{1}: x^{2} + y^{2} = R^{2}) is easier. The equation in this case is that of a conic, and takes the form Ax^{2} + 2Bx + Cy^{2} + D = 0, where

A = R^{2} + a^{2}, B = a(r^{2}-a^{2}-R^{2}), C = R^{2}, D = (R^{2}a^{2} + r^{4} + 2r^{2}a^{3} + a^{4}).